A Fully Coupled Sensitivity Analysis Framework for Offshore Wind Turbines Based on an XGBoost Surrogate Model and the Interpretation of SHAP

Abstract

To advance global sustainability and meet climate targets, the development of reliable renewable energy infrastructure is paramount. Offshore wind energy is a key factor in achieving this goal, and ensuring its operational efficiency requires a deep understanding of the sources of uncertainty faced by offshore wind turbines (OWTs). This study proposes and implements an integrated framework for sensitivity analysis (SA) to investigate the key sources of uncertainty influencing the dynamic response of an OWT. This framework is based on the XGBoost surrogate model and Sobol’s method, aiming to efficiently and accurately quantify the impact of various uncertain parameters. A key methodological novelty lies in the integrated use of Sobol’s method and SHapley Additive exPlanations (SHAP), which provides a unique cross-validating mechanism for the sensitivity results. This study demonstrates the strongly condition-dependent nature of the OWT’s sensitivity characteristics by analyzing design load cases. The results indicate that wind speed is the dominant factor influencing the structural response under normal operating conditions. In contrast, under extreme shutdown conditions, the response of the OWT is primarily governed by the physical and material properties of the structure. In addition, the high consistency between the results of SHAP technology and the SA results obtained by Sobol’s method confirms the reliability of the proposed framework. The identified key sources of uncertainty provide direct practical insights for design optimization and reliability assessment of OWTs.

1. Introduction

The global pursuit of sustainable development has intensified the urgency to transition toward renewable energy sources, driven by escalating energy demands and the finite nature of fossil fuels [1]. Renewable energy offers a viable pathway to address future energy security while significantly mitigating greenhouse gas emissions, preserving ecological balance, and generating substantial employment opportunities [2,3]. Recognizing these benefits, countries around the world are intensifying their efforts to advance the adoption and integration of renewable energy [4,5].

Renowned for its powerful wind resources, offshore wind energy plays a pivotal role in the renewable sector and serves as a cornerstone for the global shift toward a sustainable and decarbonized energy future [6]. This alignment with critical sustainability objectives is the key catalyst behind the sector’s unprecedented growth and technological innovation. Based on the Global Wind Energy Council’s “Global Wind Report 2025,” the cumulative installed capacity of offshore wind power worldwide reached approximately 83.2 GW as of 2024 [7]. Global installed capacity continues to increase rapidly, with significant annual additions concentrated primarily in established markets such as Europe and China, and growing interest extending to North America and the Asia-Pacific region. Technological advancements, particularly in turbine size and floating foundation concepts for deeper waters, are continuously pushing the boundaries of feasibility and energy yield [8,9,10]. This momentum highlights the critical role of offshore wind energy in achieving ambitious national and international renewable energy targets [11].

Despite its immense potential, the successful and cost-effective deployment of offshore wind energy faces significant engineering and economic challenges. Among various foundation types, the monopile remains the predominant and most mature solution for many projects installed in relatively shallow to intermediate water depths (typically up to 30–40 m). Its simplicity in design and installation contributes to its widespread adoption [12]. However, the monopile-supported offshore wind turbine (OWT) is a highly complex, dynamically sensitive system [13]. Its structural response and long-term performance are influenced by various interacting factors, including environmental loads, structural geometry, and other parameters [14]. The inherent uncertainties in input parameters and their complex interactions often lead to structural designs that are either overly conservative or pose safety risks. Therefore, it is crucial to identify the parameters that have a decisive impact on key response indicators.

A common approach involves using sensitivity analysis (SA) to identify specific design variables that significantly affect structural response, systematically addressing this requirement. The fundamental concept of SA is to measure the rate of change in system response caused by minor disturbances in any design variable [15]. SA methods have been applied in the design of OWTs to identify the dominant variables that significantly impact the system’s dynamic response. Thapa et al. [16] proposed an SA framework that considers numerous uncertain parameters and examined the finite element model of composite blades. Shittu et al. [17] performed SA on the random variables applied to the OWT jacket support structure, and the results indicated that wind speed uncertainty was the primary influencing factor. The OWT was modeled using the finite element method, and the rotor–nacelle assembly (RNA) was simplified as concentrated masses. Glišić et al. [18] conducted SA on the fatigue stress of an OWT supported by a single pile, using a finite element model that excluded the RNA. They showed that hydrodynamic parameters have a greater impact on the structure.

In order to compensate for the insufficient consideration of OWT coupling effects in the aforementioned studies, several aero-servo-hydro-elastic simulation tools were employed to model the time-domain structural response of OWTs during SA execution. Using OpenFAST, Han et al. [15] performed a reliability-based SA on a 5 MW monopile-supported OWT; the results indicated that environmental loads have the most significant influence on failure due to excessive deflection. Similarly, Velarde et al. [19] conducted dynamic simulations and SA in HAWC2 for a 5 MW monopile-supported OWT, which confirmed the critical role of environmental parameters in affecting the fatigue loads of OWT support structures.

Conducting SA directly on high-fidelity finite element models of OWTs is often computationally prohibitive due to the complexity of the systems and the large number of simulations required. To overcome this challenge, surrogate models are widely employed as efficient approximations of the computationally expensive high-fidelity models. There are currently multiple algorithms available, including Kriging [20,21], artificial neural networks [22,23], Gaussian process regression [24,25], XGBoost [26,27], and others.

The application of XGBoost in OWT research has significant advantages. The high nonlinearity and strong coupling of OWT operation data pose severe challenges to the model, and XGBoost’s ability to capture complex relationships and prevent overfitting makes it an ideal choice for solving such problems. Cakiroglu et al. [28] compared the power prediction performance of various models for OWTs, and the results showed that the XGBoost algorithm had the best performance. They also pointed out that wind speed was the most significant input feature of the SHAP algorithm for model prediction. However, the feature importance provided by SHAP values is only an explanation for “model prediction”, and further verification is needed for the explanation of physical relationships [29]. Therefore, this study proposes an improved comprehensive framework for OWT SA, whose core is a Sobol–SHAP ensemble method that cross-verifies the accuracy of interpretation results and SA results from a methodological perspective.

2. Framework for Conducting a Sensitivity Analysis on Offshore Wind Turbines

2.1. Brief Introduction to the Sensitivity Analysis Framework

This study integrates the three core stages of SA for an OWT: initialization, fully coupled dynamic time-domain simulation, and parameter SA. Based on this structure, a universal, fully coupled SA framework is established (Figure 1), whose execution process is divided into six key steps based on functional differences.

(1)

The identification of uncertain variables for an OWT is the cornerstone and prerequisite for performing SA. As the primary sources of variability in the system’s response, their accurate definition directly determines the reliability and validity of the analysis results. These uncertainties include both external environmental variables at the OWT’s operational site and internal structural, geometric, and material parameters of the turbine itself [30,31,32]. Once identified, determining the distribution type and statistical characteristics for each key variable becomes the central task in quantifying uncertainty. This statistical data provides the essential input for the subsequent fully coupled dynamic simulations.

(2)

Based on the uncertainty variables identified in step 1 and their statistical characteristics, this step constructs an input parameter space that can represent all combinations of uncertainty through the development of an efficient sampling strategy. The primary objective of this process is to generate representative sample points for subsequent fully coupled dynamic simulations. This study employs the Latin Hypercube Sampling (LHS) [33] method. As an advanced stratified sampling technique, LHS is particularly suitable for multivariate analysis and offers considerable advantages over traditional Monte Carlo Sampling (MCS) [34,35] in terms of sampling efficiency. It should be noted that quasi-random sequences can achieve an even lower discrepancy and potentially higher convergence rate than LHS under the same sample size [36,37,38]. Nevertheless, LHS was retained here for its simple implementation and well-established performance in similar applications.

(3)

In theory, increasing the number of samples generated in step 2 enhances the accuracy of the uncertainty space representation. However, this also substantially increases computational costs, as each sample combination necessitates a complete, nonlinear, fully coupled dynamic simulation. An automated simulation execution module was developed to address this challenge and ensure analytical efficiency. The core function of this module is to seamlessly integrate the sampling and simulation stages. It automatically reads the sample matrix generated by LHS and produces corresponding simulation models by batch-modifying the base model files. It then invokes the numerical simulation software to conduct fully automated time-domain dynamic coupling analyses, eliminating the need for manual intervention.

The dynamic analysis in this study is conducted using OrcaFlex (version 11.5b) software. OrcaFlex, developed by Orcina [39,40], is a leading commercial software package for dynamic analysis in marine engineering systems. It accurately simulates the coupled dynamic response of OWTs in complex marine environments. Numerical simulations are efficiently executed by integrating the automation module with OrcaFlex, providing a sufficient data foundation for the subsequent SA.

(4)

After completing all time-domain dynamic coupling analyses, dynamic response indicators relevant to structural safety are collected for use in the subsequent SA. The structural dynamic response extracted in this study includes front-aft (F-A) displacement at the tower top, maximum von Mises stress at the tower base, F-A bending moment at the tower base, F-A displacement at the monopile top, and pitch angle at the monopile top.

(5)

Before performing SA, it is essential to construct a surrogate model that effectively captures the nonlinear relationship between the input uncertainty variables and the output structural response. Global SA methods, such as analysis of variance (ANOVA) or Sobol’s method, typically require tens of thousands of model evaluations to yield convergent results. Conducting the tens of thousands of model evaluations required for global SA using the high-fidelity OrcaFlex model directly would be computationally prohibitive. A surrogate model is a computationally efficient mathematical approximation of the original simulation. It replaces the original simulation model with minimal computational overhead, enabling structural response prediction of any input parameter combination within milliseconds [41,42,43,44]. This facilitates the application of global SA, which will otherwise be impractical due to excessive computational demands. This study employs the Extreme Gradient Boosting (XGBoost) machine learning model as the surrogate model [45]. Feature contribution analysis is then performed on its predictions and compared to the SA results for validation.

(6)

With a high-fidelity surrogate model established and validated, the final step of the framework involves executing the SA. This step quantitatively evaluates the contribution of each uncertain input variable to the variance of the OWT’s structural response. The variance-based Sobol method [46] is utilized in this study to complete this task. Tens of thousands, or more, model evaluations are conducted at negligible computational cost, utilizing the computational efficiency of the surrogate model to ensure.

2.2. Sampling of Random Variables

The primary objective of sampling methods is to comprehensively and unbiasedly explore the entire parameter space using a limited number of sample points. In this study, the LHS method was employed. LHS is an efficient stratified sampling technique, particularly well-suited for high-dimensional problems involving computationally expensive models. The core idea of LHS is to enforce uniform sampling within the full probability distribution range of each input uncertainty variable.

LHS was performed by first stratifying the cumulative distribution function of each input variable into N non-overlapping intervals of equal probability [47,48,49]. A value was randomly selected from each interval and transformed into a physical sample value using the inverse cumulative distribution function (CDF). The N samples for each variable were then randomly combined to generate the required set of input vectors.

For computationally expensive time-domain dynamic simulations of OWTs, LHS provides higher sampling efficiency, superior space-filling properties, and faster convergence compared to MCS. These advantages make LHS a suitable sampling technique for the SA of complex systems such as OWTs.

2.3. Fully Coupled Dynamic Time Domain Simulation of OWTs

The high-fidelity, fully coupled, time-domain simulation serves as the critical link between the defined uncertain variables and the dynamic responses of the OWT. The fidelity of this simulation stage is crucial, as it directly influences the quality of the dataset utilized to train the subsequent surrogate model.

This research utilizes OrcaFlex (v. 11.5b), a commercial software package developed by Orcina. OrcaFlex was chosen for its comprehensive, validated capabilities and its well-established reputation in the offshore industry. The software enables fully coupled analysis by integrating the governing physics of multiple interacting subsystems, including aerodynamics, hydrodynamics, structural dynamics, mooring and foundation responses, as well as the turbine’s control system. OrcaFlex effectively captures the transient and coupled dynamic characteristics of the OWT by numerically solving the complete nonlinear equations of motion in the time domain [50,51].

In addition, an SA framework requires a substantial number of simulations to accurately map the relationship between the stochastic inputs and the dynamic response of the OWT. Implementing an automated, parametric modeling workflow is essential for handling this computational demand. This approach minimizes manual operational errors and significantly improves research efficiency. OrcaFlex supports this through its robust Application Programming Interface (API), which is compatible with languages such as Python (v 3.12). The API allows for programmatic control over the entire simulation process, including the batch generation of model files based on sampled parameters, automated execution, and extraction of time-series results.

2.4. Surrogate Model

This study introduces surrogate model technology to perform global SA at an acceptable computational cost. The primary function of the surrogate model is to learn and replicate the input-output relationships of high-fidelity numerical models, enabling the execution of numerous repetitive evaluations at minimal computational expense. In this study, the surrogate model was developed using the XGBoost algorithm.

XGBoost is an efficient and scalable implementation of the gradient boosting decision tree algorithm, developed by Chen and Guestrin [52] in 2016. As an advanced ensemble learning technique, XGBoost combines predictions from multiple weak learners (typically decision trees) to form a robust predictive model. XGBoost is renowned for its high prediction accuracy, computational efficiency, and resistance to overfitting. It has demonstrated outstanding performance in various machine learning competitions and industrial applications, making it highly suitable for building surrogate models for complex engineering systems [53].

The modeling process of XGBoost is iterative and additive. The core idea is that the model sequentially adds decision trees, with each new tree aimed at correcting the accumulated prediction residuals from all previously added trees. If the model’s predicted value is $y_i$, for a given input sample $x_i$, then the model’s prediction can be expressed at the t-th iteration as follows:

$${\widehat{y}}_i^t={\widehat{y}}_i^{t-1}+f_t(x_i)$$

(1)

where ${\widehat{y}}_i^{t-1}$ is the accumulated prediction result of the first t − 1 trees, while $f_t\left(x_i\right)$ is the newly generated decision tree model in this iteration.

Compared to traditional gradient boosting algorithms, the superiority of XGBoost is mainly reflected in its rigorously designed objective function:

$$Ob{j}^{(t)}={\displaystyle \sum _{i=1}^{n}l(y_i,{\widehat{y}}_i^{t-1}+f_t(x_i))+\Omega (f_t)}$$

(2)

which is composed of two parts: the loss function $l(y_i,{\widehat{y}}_i^{t-1}+f_t\left(x_i\right))$ and regularization term $\mathsf{\Omega }\left(f_t\right)$. The loss function $l(y_i,{\widehat{y}}_i^{t-1}+f_t\left(x_i\right))$ quantifies the discrepancy between the model’s predicted values and the true values. This study employs the mean square error (MSE) as the loss function. The regularization term $\mathsf{\Omega }\left(f_t\right)$ is defined by Equation (3) to penalize model complexity and prevent overfitting, and it also comprises two components.

$$\Omega (f_t)=\gamma T+{\displaystyle \frac{1}{2}}\lambda {\displaystyle \sum _{j=1}^T{w}_j^2}$$

(3)

where T is the number of leaf nodes in the decision tree, $w_j$ is the weight (i.e., prediction score) of each leaf node; $\gamma$ and $\lambda$ are hyperparameters controlling the regularization strength. XGBoost effectively mitigates model overfitting and enhances generalization performance by incorporating this regularization term.

Although the XGBoost model demonstrates good predictive performance, its internal mechanism operates similarly to a “black box”, making it challenging to intuitively discern how specific input variables influence the final prediction results. Therefore, the present study applies the SHapley Additive exPlanations (SHAP) technique to perform an interpretability analysis on the trained XGBoost surrogate model.

SHAP is a model interpretation framework introduced by Lundberg and Lee [54] in 2017, grounded in the Shapley Value from cooperative game theory. The central concept of the Shapley Value is to allocate benefits equitably among participants in a collaborative setting based on each participant’s marginal contribution to the overall outcome. SHAP innovatively transfers this concept to machine learning models by framing the prediction process as a “cooperative game” where each input feature (uncertainty variable) acts as a “participant” and the model’s final predicted value represents the “total benefit”. The SHAP value quantifies the contribution of a specific feature to an individual prediction. At the core of the SHAP explanation model lies an additive feature attribution structure, represented in the following form:

$$g(z^{\prime })={\varphi }_0+{\displaystyle \sum _{i=1}^M{\varphi }_i{z}_i^{\prime }}$$

(4)

where g is the explanatory model, $z^{\mathrm{\prime }}$ is the simplified input feature (usually indicating whether the feature exists), M is the number of input features, ${\varphi }_0$ is the baseline prediction value of the model (the mean of all training sample predictions), and ${\varphi }_i$ is the SHAP value of the i-th feature.

2.5. Global Sensitivity Analysis Method

This study employs Sobol’s method [46] for global SA to quantitatively assess the influence of various uncertain input variables on the variance of the OWT structural response. Sobol’s method, a variance-based global SA approach, is widely regarded as one of the most robust and comprehensive techniques due to its ability to capture nonlinearities and variable interaction effects [55,56]. Although the form used in this article is still the benchmark method, it should be pointed out that this method has made some valuable improvements in recent years [57,58,59], aimed at improving computational efficiency and expanding application scenarios.

The fundamental principle of Sobol’s method is the decomposition of the total variance V(Y) of the model output into partial variances attributable to individual input variables, pairwise interactions, higher-order interactions, and beyond. If the model can be represented as $Y=f(X_1,X_2,···,X_k)$, the total variance can be uniquely broken down as follows:

$$V(Y)={\displaystyle \sum _{i=1}^k{V}_i+{\displaystyle \sum _{1\le i<j\le k}^k{V}_{ij}+\cdots +V_{1,2,\dots ,k}}}$$

(5)

where $V_i$ is the output variance caused by the individual variation in the input variable $X_i$; $V_{ij}$ is the interaction part caused by the joint variation of $X_i$ and $X_j$, excluding their individual effects, and others.

Sobol’s method defines two principal indices: the first-order Sobol index, which quantifies the isolated contribution of an input variable $X_i$ to output uncertainty, and the total-effect Sobol index, which captures the overall contribution of $X_i$, including all interaction effects with other variables. These indices are formally presented in Equations (6) and (7), respectively.

$$S_i={\displaystyle \frac{V_i}{V(Y)}}={\displaystyle \frac{V[E(Y|X_i)]}{V(Y)}}$$

(6)

$$S_{T_i}={\displaystyle \frac{E[V(Y|X_{~i})]}{V(Y)}}=1-{\displaystyle \frac{V[E(Y|X_{~i})}{V(Y)}}$$

(7)

3. Benchmark OWT and Environmental Conditions

3.1. Benchmark OWT Description

The OWT model examined in this study is based on the IEA 10 MW reference turbine developed by Bortolotti et al. [60]. A schematic representation of the monopile-supported OWT is provided in Figure 2, while the primary technical specifications of the OWT system are systematically listed in

Table 1. Key technical specifications of the OWT system.

Property	Description
Rated power	10 MW
Key technical specifications of the OWT system	Upwind, 3 blades
Cut-in, rated, and cut-out wind speed	4, 11, and 25 m/s
Cut-in and rated rotor speed	6 and 8.68 rpm
Tower base elevation above mean sea level	10 m
Tower height	105.63 m
Tower top diameter, thickness	5.5 m, 0.03 m
Tower base diameter, thickness	8.3 m, 0.07 m
Monopile diameter, thickness	9.0 m, 0.1 m

.

A fully coupled model of the offshore wind turbine was developed in OrcaFlex. The tower was discretized into 21 cylindrical segments with linearly interpolated outer diameters and wall thicknesses. The monopile was also modeled as a cylindrical element with its respective geometric and structural properties. The blades were represented using lumped mass points and massless beam elements to capture aero-elastic coupling effects. The rotor was simulated using OrcaFlex’s “turbine” component, with the nacelle defined as a 6-DOF rigid body. The controller was implemented via an external Python function interfacing with the NREL ROSCO controller Dynamic Link Library (DLL).

3.2. Design Load Condition and Random Variables

Morató et al. [61] systematically analyzed the limit state load conditions in the IEC 61400-3 [62] standard and identified the most influential subset of operating conditions in terms of key design parameters. Based on their authoritative rankings, this study selected the top three random load conditions, namely DLC 1.3, DLC 1.6a, and DLC 6.2a. These three working conditions are widely regarded as the most critical and representative working conditions in the safety assessment of OWT structures, and have been adopted in many important studies in this field [63,64]. The selected load cases are listed in

Table 2. Design load cases (DLCs).

Element	DLC 1.3	DLC 1.6a	DLC 6.2a
Operation state	Power production	Power production	Parked
Wind model	ETM	NTM	EWM
Wind speed	14 m/s	12 m/s	40.375 m/s
Wave model	NSS	SSS	ESS
$\mathrm{Wave} \left(H_s\right|T_p$)	1.91 m|6.07 s	8.07 m|11.3 s	8.07 m|11.3 s
Current model	NCM	NCM	ECM
Current speed	0.6 m/s	0.6 m/s	1.2 m/s
Wind/wave misalignment	0°	0°	0°

.

Table 3. Statistical parameters of random variables.

Parameter	Dist.	Mean	Cov.	Ref.
$\mathrm{Wind} \mathrm{speed}, V_w$ (m/s)	Normal	Table 2	0.05	[63]
$\mathrm{Significant} \mathrm{wave} \mathrm{height}, H_s$ (m)	Normal	Table 2	0.05	[63]
$\mathrm{Peak} \mathrm{spectral} \mathrm{period}, T_p$ (s)	Normal	Table 2	0.05	[63]
$\mathrm{Current} \mathrm{speed}, V_c$ (m/s)	Normal	Table 2	0.05	[63]
$\mathrm{Young}’\mathrm{s} \mathrm{modulus} \mathrm{of} \mathrm{tower}, E_t$ (GPa)	Lognormal	210	0.03	[15,65,66]
$\mathrm{Young}’\mathrm{s} \mathrm{modulus} \mathrm{of} \mathrm{monopile}, E_m$ (GPa)	Lognormal	210	0.03	[15,65,66]
$\mathrm{Tower} \mathrm{thickness}, t_t$ (m)	Normal	Figure 2	0.03	[63,67]
$\mathrm{Monopile} \mathrm{thickness}, t_m$ (m)	Normal	Figure 2	0.03	[63,67]

provides the random variables considered in SA under these load conditions.

Environmental conditions are generated numerically: turbulent wind fields are simulated using the TurbSim software (v 2.00.08a-bjj) based on the Kaimal spectrum; irregular waves follow the JONSWAP spectrum; and current conditions are modeled using a near-surface profile. The first 120 s of each simulation are excluded to eliminate initial transient behavior. For each operational condition, six simulations are executed using different random seeds, and the structural response is defined as the average of these six runs, minimizing the impact of stochastic variability.

DLC 1.3 is characterized by the application of the Extreme Turbulence Model (ETM), Normal Sea State (NSS), and Normal Current Model (NCM). 1500 simulations were conducted to generate a comprehensive dataset, covering 250 distinct operational conditions, with six unique random seeds applied to each condition. Each simulation runs for 720 s, with the initial 120 s of transient behavior excluded from the analysis. The resulting dataset is divided for model development: 70% is allocated for training, 15% for parameter validation, and the remaining 15% for final performance evaluation.

The Normal Turbulence Model (NTM) was utilized in DLC 1.6a for typical operating conditions. The model also incorporates Severe Sea State (SSS) criteria to account for extreme environments. The selected SSS is defined by the significant wave height with a 50-year return period. Using a simulation duration of 1 h, the significant wave height ($H_s$) of the period is determined by applying a conversion factor of 1.09 to the reference period value of 3 h [62]. This yields a once-in-50-year wave height ($H_{s50}$) of 8.07 m and a peak period ($T_p$) of 11.3 s. A total of 150 samples were selected for 900 simulations (using 6 seeds and 150 simulations per seed) to manage computational requirements. Each simulation runs for 3720 s, with the first 120 s discarded. A total of 70% of the final dataset is used for model training, 15% is allocated for adjusting model parameters in the validation set, and the remaining 15% is reserved for final performance testing.

DLC 6.2a simulates a parked configuration, addressing the necessity to prevent potential rotor damage from extreme winds. The Extreme Wind Model (EWM) is employed to characterize wind conditions, representing severe wind scenarios. Simultaneously, the Extreme Sea State (ESS) is utilized to define the sea conditions, characterized by its 50-year significant wave height and peak period, which indicate the most challenging oceanic environments. Consistent with DLC 1.6a, the dynamic simulation lasts for 3720 s, excluding the initial 120 s, and 150 samples were selected for 900 simulations (using 6 seeds and 150 simulations per seed).

4. Application Example

4.1. Validation of Surrogate Models

Ensuring the predictive fidelity of surrogate models is paramount for achieving robust and trustworthy computational outcomes. Carefully extracted engineering response parameters that reflect structural safety include F-A displacement at the tower top, maximum von Mises stress at the tower base, F-A bending moment at the tower base, F-A displacement at the monopile top, and pitch angle at the monopile top. Proposing the maximum value of the time series as the dataset, we divide it as follows to rigorously train and evaluate the surrogate model: 70% is allocated for training the model, 15% is reserved for validation (hyperparameter tuning and model selection), and the remaining 15% is strictly withheld as the final test set, ensuring it remains completely unseen by the model during both the training and validation phases to provide an unbiased assessment of its generalization capability.

The normalized root mean square error (NRMSE), defined in Equation (8), is the primary performance metric to quantify the predictive accuracy of the surrogate model. To further bolster confidence in the model’s robustness and mitigate the risk of overfitting, a 5-fold cross-validation procedure was implemented.

Table 4. NRMSE performance of XGBoost model on cross-validation and test set.

	Tower Top F-A Displacement		Tower Base Von Mises Stress		Tower Base F-A Bending Moment		Monopile Top F-A Displacement		Monopile Top Pitch Angle
	CV 1	TV 2	CV	TV	CV	TV	CV	TV	CV	TV
DLC 1.3	0.91 $\pm$ 0.12% 3	0.87%	0.87 $\pm$ 0.1%	0.85%	1.3 $\pm$ 0.15%	1.12%	1.49 $\pm$ 0.18%	1.55%	1.29 $\pm$ 0.11%	1.27%
DLC 1.6a	1.94 $\pm$ 0.21%	1.97%	1.68 $\pm$ 0.18%	1.52%	2.11 $\pm$ 0.25%	1.8%	2.55 $\pm$ 0.27%	2.68%	2.76 $\pm$ 0.21%	2.83%
DLC 6.2a	1.3 $\pm$ 0.16%	1.27%	0.78 $\pm$ 0.13%	0.69%	0.71 $\pm$ 0.11%	0.79%	2.12 $\pm$ 0.27%	2.17%	1.81 $\pm$ 0.25%	1.95%

¹ cross-validation. ² Test set validation. ³ average performance indicators and their standard deviations.

presents the results of cross-validation (average performance indicators and their standard deviations) under three design load conditions, as well as the final NRMSE values predicted by surrogate models for independent test sets.

$$NRMSE={\displaystyle \frac{\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{(y_i^{\ast }-y_i)}^2}}}{\frac{1}{n}{\displaystyle \sum _{i=1}^n{y}_i}}}$$

(8)

where n is the number of validation samples; $y_i^{\mathrm{*}}$ and $y_i$ are the predicted and actual values, respectively.

As summarized in Table 4, the NRMSE values for all key responses across the three design load cases are consistently below 3%. This high predictive accuracy, corroborated by 5-fold cross-validation, confidently demonstrates that the developed XGBoost surrogate models possess sufficient fidelity for the subsequent global SA.

4.2. Sensitivity Analysis

This chapter presents a detailed SA of the dynamic response of the OWT.

Table 5. SA results of DLC 1.3.

	${\mathit{H}}_{\mathit{s}}$	${\mathit{T}}_{\mathit{p}}$	${\mathit{V}}_{\mathit{w}}$	${\mathit{V}}_{\mathit{c}}$	${\mathit{E}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{m}}$	${\mathit{E}}_{\mathit{m}}$
Tower top F-A displacement	0.005	0.008	0.634	0.006	0.116	0.092	0.098	0.075
Tower base von Mises stress	0.005	0.010	0.265	0.013	0.053	0.658	0.016	0.017
Tower base F-A bending moment	0.002	0.003	0.889	0.003	0.064	0.049	0.005	0.010
Monopile top F-A displacement	0.001	0.007	0.419	0.001	0.004	0.005	0.315	0.267
Monopile top pitch angle	0.001	0.007	0.407	0.002	0.005	0.007	0.311	0.273

indicates that Sobol’s method is employed to calculate sensitivity indices for DLC 1.3. These indices are utilized to identify the uncertainty variables that exhibit the highest impact on each response indicator.

SHAP values provide a methodology for quantifying the contribution of input features to model predictions. The SHAP summary plot in Figure 3 illustrates the impact of these random variables on the predicted response of DLC 1.3. In this plot, the vertical ordering of the variables reflects their relative importance, with features exerting greater influence positioned higher.

Table 5 and Figure 3 exhibit that the wind speed ($V_w$) is the most important sensitivity parameter for tower top F-A displacement, followed by tower Young’s modulus ($E_t$), monopile thickness ($t_m$), tower thickness ($t_t$), and monopile Young’s modulus ($E_m$). In addition, the Sobol index results are highly consistent with the SHAP value results. The tower thickness ($t_t$) demonstrates an overwhelming influence on tower base von Mises stress, indicating that the structural dimensions of the tower play a decisive role in its stress level. Similarly to tower top F-A displacement, for tower base F-A bending moment, wind speed ($V_w$) is the most critical variable. In addition, discrepancies exist between the SA and SHAP results regarding the ranking of wave height ($H_s$), wave period ($T_p$), current speed ($V_c$), and monopile thickness ($t_m$). This divergence arises from the relatively minor influence of these three variables, combined with inherent differences between the two methods. However, both methods exhibit strong agreement in identifying the dominant variables. For the two responses directly related to the foundation, namely monopile top F-A displacement and monopile top pitch angle, wind speed ($V_w$) is identified as the most influential factor. The thickness ($t_m$) and Young’s modulus ($E_m$) of the monopile are secondary but significant influencing factors.

The SA results and SHAP values of DLC 1.6a are listed in

Table 6. SA results of DLC 1.6a.

	${\mathit{H}}_{\mathit{s}}$	${\mathit{T}}_{\mathit{p}}$	${\mathit{V}}_{\mathit{w}}$	${\mathit{V}}_{\mathit{c}}$	${\mathit{E}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{m}}$	${\mathit{E}}_{\mathit{m}}$
Tower top F-A displacement	0.006	0.014	0.625	0.003	0.088	0.101	0.076	0.122
Tower base von Mises stress	0.003	0.003	0.537	0.002	0.009	0.446	0.004	0.011
Tower base F-A bending moment	0.016	0.014	0.904	0.007	0.039	0.029	0.003	0.010
Monopile top F-A displacement	0.091	0.062	0.185	0.013	0.010	0.004	0.285	0.410
Monopile top pitch angle	0.022	0.029	0.249	0.001	0.003	0.002	0.315	0.393

and Figure 4, respectively. Wind speed exerts a dominant influence on the OWT’s response, significantly surpassing the impact of other parameters. This dominance arises from the specific wind speed of 12 m/s, which closely approaches the turbine’s rated wind speed. Hence, wind speed influences the structural response more substantially than the DLC 1.3 condition itself, leading to a relatively large aerodynamic thrust.

DLC 6.2 corresponds to the shutdown survival condition under an extreme wind speed ($V_w$ = 40.375 m/s) in conjunction with extreme sea states. In this condition, the wind turbine blades are positioned in the feathered state to minimize loads.

Table 7. SA results of DLC 6.2a.

	${\mathit{H}}_{\mathit{s}}$	${\mathit{T}}_{\mathit{p}}$	${\mathit{V}}_{\mathit{w}}$	${\mathit{V}}_{\mathit{c}}$	${\mathit{E}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{t}}$	${\mathit{t}}_{\mathit{m}}$	${\mathit{E}}_{\mathit{m}}$
Tower top F-A displacement	0.005	0.002	0.006	0.002	0.313	0.325	0.199	0.172
Tower base von Mises stress	0.002	0.002	0.001	0.001	0.002	0.985	0.001	0.002
Tower base F-A bending moment	0.007	0.108	0.074	0.005	0.612	0.047	0.124	0.068
Monopile top F-A displacement	0.005	0.001	~	0.001	0.001	0.003	0.538	0.460
Monopile top pitch angle	0.003	0.001	0.004	0.002	0.002	0.003	0.557	0.453

and Figure 5 reveal that the sensitivity characteristics of the system underwent a fundamental shift under the shutdown survival condition. The dominant source of uncertainty transitions from aerodynamic loads during normal operation to the structural and material properties themselves.

In order to further explore the physical reasons for the high sensitivity of structural parameters under DLC 6.2a, this study compares the dynamic response characteristics under different design load cases. The frequency domain analysis results shown in Figure 6 indicate that under both DLC 1.3 and DLC 1.6a—representing operational states— the dynamic response is co-dominated by the structure’s first tower F-A natural frequency and the 3P frequency. In contrast, when the OWT is in a stopped state (DLC 6.2a), the dynamic response is primarily dominated by its natural frequency due to the negligible rotor thrust acting on the feathered blades and the consequent absence of significant 3P excitation. Han et al. [68]’s research shows that the natural frequency of a structure is highly sensitive to changes in parameters such as Young’s modulus and component thickness. Therefore, in the DLC 6.2a operating condition dominated by natural frequency response, the global sensitivity of these parameters that determine the basic dynamic characteristics of the structure will significantly increase.

5. Conclusions and Future Work

This study establishes and applies an integrated, fully coupled framework for Global SA to systematically identify and quantify the key uncertain parameters influencing the dynamic response of an OWT. The proposed framework integrates high-fidelity numerical simulations, efficient sampling techniques, and advanced machine learning methods, providing a robust and computationally efficient approach for the SA of complex offshore engineering systems.

The main findings of this study are as follows:

1.

The sensitivity characteristics of the OWT strongly depend on the operational conditions. Under normal operating conditions (DLC 1.3 and DLC 1.6a), the system’s dynamic responses are primarily governed by external environmental variables, with wind speed identified as the most influential parameter. This indicates that an accurate characterization of the wind speed is paramount for structural performance assessment during power production.

2.

A significant shift in the dominant sources of uncertainty is observed under shutdown survival conditions (DLC 6.2a). When the OWT is parked and feathered to endure extreme wind and wave events, its dynamic response is governed almost entirely by structural and material properties. The direct impact of environmental parameters becomes secondary. This result highlights the necessity of precise control over structural tolerances and material quality to ensure system survivability during ultimate limit states.

3.

The cross-validation of methodologies confirms the high reliability of the research findings. Two analytical methods grounded in entirely different theoretical foundations, Sobol’s method and SHAP values, produce a consistent ranking of the importance of the uncertain variables. This strong agreement not only validates the accuracy of the constructed XGBoost surrogate model but also provides robust, dual-source confidence in the conclusions of the SA.

Accordingly, this research clarifies the key physical factors influencing the OWT’s dynamic response across various operational phases and demonstrates the powerful capability of an advanced and efficient analytical framework. The results provide direct guidance for refining the design, assessing risk, and optimizing the life-cycle reliability of OWTs. Engineers can prioritize and tighten the tolerance and control of key parameters based on sensitivity ranking under different working conditions. In particular, the collection of meteorological condition parameters in the area where the OWT is located is considered to evaluate the situation of OWT encountering downtime in order to achieve targeted design and optimization of structural parameters and material selection. In addition, these parameters should be established as core variables for probabilistic design and reliability analysis, providing a critical data foundation for calibrating sub-item safety factors in standards such as IEC 61400-3 based on reliability theory.

In future research, the authors will focus on refining the coupling model and expanding the scope of validation. Specifically, future studies will consider the statistical correlation between wind wave misalignment effects and environmental loads and introduce the soil-structure interaction (SSI) model. In addition, the effectiveness of the framework will be validated through pool tests or on-site monitoring data, and its applicability will be extended to other types of OWTs (floating wind turbines, jacket structures, etc.) to verify its reliability and application value in a wider range of engineering practices.